I would actually argue that wikipedia, newspaper like the Times etc are acting as a press. Therefore covered by the amendment's specific mention thereof. Don't even need to invoke the freedom of speech of those who did the actual writing. You still could however[1].

The ISPs aren't acting as a press, unless they wish to assert that their primary objective is to publish IPs and other metadata. That is fine as well but they should then lose protection as a simple carrier of data. They would also incur liability of what is published. I'm fair sure they wouldn't want that. They would scream "we're not a press we're a carrier!" to escape that liability.

This is similar to the postal service asserting that they are a press and then selling delivery details or even opening your letters and sharing their content. So, what business are they in? Publisher or carrier? I think it matters.

[1] The weaker fallback of a corporation using its employee's freedom of speech asserts that those employees are fully protected from the corporation. I doubt that is ever true. So in a real way the employees don't have free rein over their opinions and speech. Restricted speakers. I'd therefore not be relying on that. I'd want wikipedia etc protected under freedom of press instead.